We investigate a hybrid optomechanical system comprised of a mechanical
oscillator and an atomic 3-level ensemble within an optical cavity. We show
that a suitably tailored cavity field response via Electromagnetically Induced
Transparency (EIT) in the atomic medium allows for strong coupling of the
mechanical mirror oscillations to the collective atomic ground-state spin. This
facilitates ground-state cooling of the mirror motion, quantum state mapping
and robust atom-mirror entanglement even for cavity widths larger than the
mechanical oscillator frequency
